The Gaussian Gabor system at the critical density is a weighted lower semi frame
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917550371110912 |
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| author | Zikkos, Elias |
| author_facet | Zikkos, Elias |
| contents | We show that the Gaussian Gabor system at the critical density is a weighted lower semi frame, thus resolving an open question. This complements recent results showing that the system is neither a weighted frame nor admits a reproducing partner. In fact, after removing any atom from the system, suitable weights produce a complete Riesz Fischer sequence and lower semi frame. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00764 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Gaussian Gabor system at the critical density is a weighted lower semi frame Zikkos, Elias Functional Analysis We show that the Gaussian Gabor system at the critical density is a weighted lower semi frame, thus resolving an open question. This complements recent results showing that the system is neither a weighted frame nor admits a reproducing partner. In fact, after removing any atom from the system, suitable weights produce a complete Riesz Fischer sequence and lower semi frame. |
| title | The Gaussian Gabor system at the critical density is a weighted lower semi frame |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2606.00764 |